1. Field
This disclosure relates to a method and system for the formation and propagation of highly nonlinear pulses with selectable pulse properties. More particularly, the present disclosure describes the generation and propagation of pulses through the use of granular chains consisting of particles with desirable geometries.
2. Description of Related Art
The existence of the highly nonlinear regime of wave propagation in solids was discovered while studying the shock absorption properties of granular matter. The model typically used to represent the simplest form of granular systems consisted of a one dimensional (1-D) chain of spherical beads regulated by Hertzian contact interaction potentials. However, a new, general wave dynamic theory, supporting compact solitary waves, was derived for all structured homogeneous materials showing a highly nonlinear force (F)−displacement (δ) response dictated by the intrinsically nonlinear potential of interaction between its fundamental components. This general nonlinear spring-type contact relation can be expressed as shown below in Eq. (1):F≅Aδn  Eq. (1)where A is a material's parameter and n is the nonlinear exponent of the fundamental components' contact interaction (with n>1). For Hertzian systems, such as those consisting of a chain of spherical beads, the n exponent of interaction is equal to 1.5.
Within the present disclosure, “granular matter” is defined as an aggregate of “particles” in elastic contact with each other, preferably in linear or network shaped arrangements. In addition to the nonlinear contact interaction present in such systems, and related purely to the particle's geometry, another unusual feature of the granular state is provided by the zero tensile strength, which introduces an additional nonlinearity (asymmetric potential) to the overall response. In the absence of static precompression acting on the systems, these properties result in a negligible linear range of the interaction forces between neighboring particles leading to a material with a characteristic sound speed equal to zero in its uncompressed state (c0=0): this has led to the introduction of the concept of “sonic vacuum”. This makes the linear and weakly nonlinear continuum approaches based on Korteveg-de Vries (KdV) equation invalid and places granular materials in a special class according to their wave dynamics. This highly nonlinear wave theory supports, in particular, a new type of compact highly tunable solitary waves that have been experimentally and numerically observed in several works for the case of 1-D Hertzian granular systems.